Gridding algorithms in Surface III

Surface III can read in numerical matrices and use these to produce contour maps, but ordinarily observations are not available neatly spaced in a uniform pattern. Especially in the natural sciences, observations usually are scattered erratically across the map area. In Surface III, as in most other contouring programs, graphic displays can be made and transformations performed only on regular arrays of points that represent the surface. Therefore, the program includes several algorithms for creating such numerical arrays from unevenly spaced data. In fact, the "gridding" of scattered data points is the single most important procedure in the graphics package.

Gridding is the estimation of values of the surface at a set of locations that are arranged in a regular pattern which completely covers the mapped area. In general, values of the surface are not known at these uniformly spaced locations, and so must be estimated from the irregularly located control points where values of the surface are known. The locations where estimates are made are referred to as "grid points" or "grid nodes."

The grid nodes usually are arranged in a square pattern so the distance between nodes in one direction is the same as the distance between them in the perpendicular direction. The spacing is under user control, and is one of many parameters that must be chosen before a surface can be gridded and mapped. The area enclosed by four grid nodes is called a "grid cell." If a large size is chosen for the grid cells, the resulting map will have low resolution and a coarse appearance, but can be computed quickly. Conversely, if the grid cells are small in size, the contour map will have a finer appearance, but will be more time consuming and expensive to produce.

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